Question

A three-hinged parabolic arch ABC has a span of 20 m and a central rise of 4.0 m. The arch has hinges at the ends and at the crown. A train of two point loads of 20 kN and 10 kN, 5 m apart, crosses this arch from left to right, with the 20 kN load leading. The maximum thrust induced at the supports is

• A. 32.81 kN
• B. 31.25 kN
• C. 25.0 kN
• D. 28.13 kN

Answer 1

The correct option is B 31.25 kN

In case of a three hinged parabolic arch, the influence line diagram for horizontal thrust is linear.

Maximum thrust will be induced at the supports when 20 kN load is at the crown.

Diagram

Ordinate of the ILD at a distance of 5 m from

$A=\frac{5}{10}\times \frac{L}{4h}=\frac{1}{2}\times \left(\frac{20}{4\times 4}\right)=0.625kN$

also $\frac{L}{4h}=\frac{20}{4\times 4}=1.25kN$